Why doesn't the mirror modifier work with object groups?
The closest that I can think of to applying a mirror modifier to a group is to use the mirror object functionality, and have the constituent objects in the group be mirrored by using the mirror object. According to the Blender manual, the definition of a mirror object is


  ... another object (usually an empty), to be used as the reference for the mirror process: its center and axes will drive the plane(s) of symmetry. You can of course animate its position/rotation to animate the mirror effect.


Otherwise, the mirror modifier is designed to be applied at the object level, and won't work at either the group level, or the mesh level.

To see how to use a mirror object, do a search of the available blender tutorials using the search parameter "mirror object".